I can get to:

1/j = v+u/uv

as per your explanation but from there I just can't figure the steps to get me to the bottom line of

u = jv/v-j

Please can you help.

>To add 1/14 and 5/6 you would first rewrite each fraction to
>have a common denominator then add the numerators of these
>fractions. The common denominator would be 42 since it is
>the least common multiple. That is 42 = 14 * 3 = 6*7. The
>principles are that 1) a fraction does not change when you
>multiply both the numerator and denominator by the same
>value and 2) the sum of any two fractions having the same
>denominator is the sum of the numerators over the common
>denominator. 1/14 = 3/42 and 5/6= 35/42 so the answer is
>(3+35)/42 or 19/21. Likewise, in the given problem, 1/T =
>U/TU and -I/U = -T/TU so the answer is (U-T)/TU.
>
> PS: As you can see, the answer you wrote had a typo so it
>is no wonder you could not figure out how it was reached.

1/j - 1/v = 1/u

Use the fraction explanation an the left side to get

(v-j)/vj = 1/u

Therefore,

vj/(v-j) = u
u = vj/(v-j)